Continuous time models of interest rate: testing peso-dollar exchange rate.

As an extension of the article by Núñez, De la Cruz and Ortega (2007), different parametric models with jumps are tested with the methodology developed by Ait-Sahalia and Peng (2006), based on the transition function. Data analyzed are the peso-dollar exchange rate. The idea is to implement continuous-time parametric models for the peso-dollar exchange rate. The results confirm that the proposed continuous time models are not good enough to explain the behavior that describes the peso-dollar exchange rate. However, considering some continuous time models with Poisson jumps is possible to describe such behavior.

Testing the Equilibrium Exchange Rate Model - Updated

We find favorable evidence for the textbook equilibrium exchange rate model of Stockman (1987) using Blanchard and Quah’s (1989) decomposition. Real shocks are shown to account for more than 90 percent of movements in the real exchange rate between Brazil and the US, and for more than half of nominal exchange rate changes. Impulse response functions also suggest that real shocks alter these countries’relative prices.Equilibrium Exchange Rate Model; Blanchard and Quah’s Decomposition

Rate optimal multiple testing procedure in high-dimensional regression

Multiple testing and variable selection have gained much attention in statistical theory and methodology research. They are dealing with the same problem of identifying the important variables among many (Jin, 2012). However, there is little overlap in the literature. Research on variable selection has been focusing on selection consistency, i.e., both type I and type II errors converging to zero. This is only possible when the signals are sufficiently strong, contrary to many modern applications. For the regime where the signals are both rare and weak, it is inevitable that a certain amount of false discoveries will be allowed, as long as some error rate can be controlled. In this paper, motivated by the research by Ji and Jin (2012) and Jin (2012) in the rare/weak regime, we extend their UPS procedure for variable selection to multiple testing. Under certain conditions, the new UPT procedure achieves the fastest convergence rate of marginal false non-discovery rates, while controlling the marginal false discovery rate at any designated level $\alpha$ asymptotically. Numerical results are provided to demonstrate the advantage of the proposed method.Comment: 27 page

Testing for monotone increasing hazard rate

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on the assumption that the null distribution is exponential. Instead, empirical information is used to effectively identify and eliminate from further consideration parts of the line where the hazard rate is clearly increasing; and to confine subsequent attention only to those parts that remain. This produces a test with greater apparent power, without the excessive conservatism of exponential-based tests. Our approach to calibration borrows from ideas used in certain tests for unimodality of a density, in that a bandwidth is increased until a distribution with the desired properties is obtained. However, the test statistic does not involve any smoothing, and is, in fact, based directly on an assessment of convexity of the distribution function, using the conventional empirical distribution. The test is shown to have optimal power properties in difficult cases, where it is called upon to detect a small departure, in the form of a bump, from monotonicity. More general theoretical properties of the test and its numerical performance are explored.Comment: Published at http://dx.doi.org/10.1214/009053605000000039 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org